How is convective heat flow calculated

CellZone · February 21, 2018, 03:40

Hi,

a) I am wondering, how convective heat flow near a wall is calculated?

So the normal way is: q = htc * (T_wall - T_fluid)

T_fluid is calculated out of the flow field , T_wall is set for example as boundary condition, so htc and q remains?

heat Transfer coefficient (htc) , I can calculate by the empirical Expression using Reynolds, Prandtlnumber and the nusselt number.

But according to the starccm guide, htc is calculated by

htc= q/ (T_wall - T_fluid)

So I am wondering where my q comes from?

b) what happens in case of an adiabatic wall, is there no convective heat Transfer? my T_wall is equal to T_fluid near the wall?

Thank you for your help!

me3840 · February 21, 2018, 09:18

a) q is calculated from fourier's law

b) an adiabatic wall means q=0, therefore dT/dx=0. So the temperature gradient at the wall must be 0, which means Twall and Tfluid of the face and first cell should be the same.

CellZone · February 21, 2018, 11:06

Thank you for your answer.

Regarding a)
So Fourier Law 1D steady state : q_x = - k *A dt/dx
So this equation is together with transport equation for heat transfer solved in the fluid domain you mean? and thus, I know my q_x near the wall?

I don't really get it how we can compute q_x near the wall. I know my heat transfer through the wall by q_x = - k *A (T_wall_left - T_wall_right) . So I can set q_x_conduction = q_x_convection = htc * (T_wall_right - T_fluid) and solve for htc?

Thanks!

me3840 · February 22, 2018, 09:37

The wall heat flux is completely defined by the solution (dT), mesh (dx and A), and the defined properties (k), so it is known at any time and space during the solution.

And then yes, you can solve for HTC in the manner you describe. Note there are multiple definitions of HTC depending on what temperatures you want to use for reference.

February 21, 2018, 03:40	How is convective heat flow calculated	#1
CellZone Member Join Date: Apr 2016 Posts: 90 Rep Power: 10	Hi, a) I am wondering, how convective heat flow near a wall is calculated? So the normal way is: q = htc * (T_wall - T_fluid) T_fluid is calculated out of the flow field , T_wall is set for example as boundary condition, so htc and q remains? heat Transfer coefficient (htc) , I can calculate by the empirical Expression using Reynolds, Prandtlnumber and the nusselt number. But according to the starccm guide, htc is calculated by htc= q/ (T_wall - T_fluid) So I am wondering where my q comes from? b) what happens in case of an adiabatic wall, is there no convective heat Transfer? my T_wall is equal to T_fluid near the wall? Thank you for your help!

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February 21, 2018, 09:18		#2
me3840 Senior Member Join Date: Nov 2010 Location: USA Posts: 1,232 Rep Power: 24	a) q is calculated from fourier's law b) an adiabatic wall means q=0, therefore dT/dx=0. So the temperature gradient at the wall must be 0, which means Twall and Tfluid of the face and first cell should be the same.

February 21, 2018, 11:06		#3
CellZone Member Join Date: Apr 2016 Posts: 90 Rep Power: 10	Thank you for your answer. Regarding a) So Fourier Law 1D steady state : q_x = - k A dt/dx So this equation is together with transport equation for heat transfer solved in the fluid domain you mean? and thus, I know my q_x near the wall? I don't really get it how we can compute q_x near the wall. I know my heat transfer through the wall by q_x = - k A (T_wall_left - T_wall_right) . So I can set q_x_conduction = q_x_convection = htc * (T_wall_right - T_fluid) and solve for htc? Thanks!

February 22, 2018, 09:37		#4
me3840 Senior Member Join Date: Nov 2010 Location: USA Posts: 1,232 Rep Power: 24	The wall heat flux is completely defined by the solution (dT), mesh (dx and A), and the defined properties (k), so it is known at any time and space during the solution. And then yes, you can solve for HTC in the manner you describe. Note there are multiple definitions of HTC depending on what temperatures you want to use for reference.